Stag varies considerably from animal to animal. Premium stag can be very expensive, especially an even coloured, dense, nicely matched pair of scales. What are you looking for? Well think of it as having two parts, an outer shell of almost white, very dense hard boney material and an inner sponge-like cortex. Depending on the health, age and general wear and tear of the animal, the thicknesses of these areas can vary. What you would like ideally, is almost all of it to be made up of that white, heavy, dense outer shell.
The inner matrix is very pourous and crumbly and doesnt make for good anything. If you have to use a piece with the inner core evident, scrape it out and fill the cavity with epoxy, or if you cant hollow it out, pour in some very thin & runny cyanoacrylate (yup, superglue). Leave it to set and then use it as normal. If you happen to expose or beak through to any of that inner matrix while shaping the outer of the handle, you can fill it with superglue.
If you are lucky, or spend a lot of money to get the good stuff, there is very little you need to do. The outer hard white stuff, is very dense and hard, it's impervious to most things, though the surface finish can surely be harmed.
For finishing, remember that the textured surface or bark is highly prized and considered very beautiful by many. If you are shaping the handle, try and leave at least *some* of that brown coloured bark, both for grip and beauty. If your stag is very white and you would prefer a more aged appearance, you can artificially colour it with - wait for it - potassium permangonate solution. Yeah, I know it's purple, but when you daub it onto wood, antler, bone or whatever, it penetrates just beneath the surface and turns a rich brown. Then just give it a rub down which will lighten it, be selective and lighten the parts where you've exposed the white of the antler, and leave those areas of outer *bark* a rich brown.
To finish, a light coat of danish oil will have a tendancy to give that exposed white boney part a more subtle ivory colour which can be very attractive. The danish oil will also fill any micro-cracks, nooks & cranny and set hard. Then just buff it with renaissance wax and you're done.
Alternatively, you could give it an all over coating with superglue, some swear by it, but I think it makes it look "plasticky".
If done well, it can look very beautiful....
as well as being fantastically durable. In a similar vien, also consider Oosic (the fossilised penis bone of a walrus), it's expensive, but makes for a very unique knife - and something of a talking point..
HTH.